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Proof step 916 from proof refine-truncate-buff-some (previous step)

# buf-opt0.buf = VFS_PAGE_SIZE, cache_icache[m3].inode = mkinode(m0, md0, false, # links(m3, cache_dirs), m10, m11), cache_files[ino] = mkfile(m8, md1, # links(ino, cache_dirs), content), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), (∅)[ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), buf-opt0.some?, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), ino ∈ cache_files, m3 ∈ cache_files, m3 ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ino ∈ cache_icache, (n ∈ content ⊕ mkcontent(ino, cache_pcache0) ↔ n ∈ content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))) ∧ ( n ∈ content ⊕ mkcontent(ino, cache_pcache0) → (content ⊕ mkcontent(ino, cache_pcache0))[n] = (content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)))[n]), m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 917:
# buf-opt0.buf = VFS_PAGE_SIZE, (∅)[ino] = mkientry(boolvar0, mkinode(m, md, boolvar, m4, m5, m7)), cache_files[m3] = mkfile(m1, md2, # links(m3, cache_dirs), content1), cache_files[ino] = mkfile(m8, md1, # links(ino, cache_dirs), content), cache_icache[m3] = mkientry(boolvar1, inode), inode = mkinode(m0, md0, false, # links(m3, cache_dirs), m10, m11), buf-opt0.some?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache0) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache0, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache0), m3 ∈ cache_icache, m3 ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache0), ∀ key. key ∈ cache_pcache0 → key.data? ⊦ ino ∈ cache_icache, m2 ≤ m6 ∧ m2 % VFS_PAGE_SIZE ≠ 0, (n ∈ content ⊕ mkcontent(ino, cache_pcache0) ↔ n ∈ content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0))) ∧ ( n ∈ content ⊕ mkcontent(ino, cache_pcache0) → (content ⊕ mkcontent(ino, cache_pcache0))[n] = (content ⊕ mkcontent(ino, truncate(m3, min(m6, m2), cache_pcache0)))[n])

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [cache_icache[m3], boolvar1, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: cache_icache[m3], boolvar1, inode